The athletic shoe manufacturer Reebok International tops the list of the nation's largest public firms in terms of long-term profitability, according to Forbes magazine's annual ranking.

Reebok, based in Canton, Mass., headed the list of 1,116 companies in 31 industries whose profitabilty was monitored in Forbes' 41st "Annual Survey of American Industry." The survey appears in the New York-based financial magazine's Jan. 9, 1989, issue.Reebok, whose owner made an abortive bid earlier in the year to buy the financially strapped New England Patriots, topped the list with a four-year average annual return on equity of more than 200 percent. However, the company is not likely to remain in that position long, the magazine warned.

"But note the latest 12-month profitability of 27.7 percent. Reebok's reign at the top won't last much longer," Forbes said. "In fact, of the 100 top-ranked corporations, 77 firms show 12-month results below their long-term performance."

Following Reebok, in order of long-term profitability, were Delta Woodside Industries, CenTrust Savings, Anchor Glass, Jepson, Microsoft, Western S&L, Pilgrim's Pride, Best Buy Co., and Chrysler.

Reebok, CenTrust Savings, Anchor Glass and Chrysler were all featured in the top 10 of Forbes' 1987 list of most profitable companies.

Public Service Company of New Hampshire, owner of the troubled Seabrook nuclear power plant, was ranked 941st and had the lowest positive return on equity, 0.2 percent. On Jan. 28, Public Service became the first investor-owned utility to seek bankruptcy protection since the Great Depression.

A Chicago-based specialized food packaging compay, Envirodyne Industries, had the highest average stock price gain - 2,322.4 percent. It was followed by Best Buy Co. (2,066.7 percent), Mayfair Super Markets (1,115.3 percent), Smithfield Foods (717.1 percent), First Capital Holding (671.4 percent), Gap (588.1 percent), Affiliated Publications (566.2 percent), Alberto Culver (533.3 percent) and Food Lion (529 percent).

Reebok also had the highest rate of earnings per share growth with a five-year average of more than 200 percent, the magazine said. It was followed, in descending order, by Anchor Glass, CalMat, Sun Microsystems and Compaq Computer.

The magazine also listed 31 companies as "the biggest turnaround candidates in 1988." Those include such well-known firms as Mattel, Gap, GTE, and General Motors Corp.

"Giant automaker GM hasn't swung completely around, but the turn signal indicator is blinking. Costs have really been cut," the magazine said.

The Atlanta-based Turner Broadcasting also made the list of turnaround candidates.

"Barely a year ago Ted Turner's Turner Broadcasting System seemed to be in big trouble, but the outlook is much brighter now. Although Turner's company is still running in the red, he has cut losses by nearly one-third, running ahead of even the most optimistic analysts' projections," the magazine said.

Forbes cited Cable News Network, Superstation TBS and the MGM film library as major factors in the broadcasting company's improved outlook.